April Problem of the Month

The Cathy Hall Show

Congratulations!  You’ve just been selected to go on The Cathy Hall Show.  On the set, there are three doors, and you are allowed to choose one. Behind one door is a car, behind another door is a goat, and behind another door is a cabbage, though of course you don’t know which is which. However, to help you, in front of each door is a TA who knows what is behind his or her door.

You can ask any TA what is behind their door any number of times you like (within the 5 minute time limit), and every time they will simply respond with either “car” or “goat” or  “cabbage.”  However one of the TA’s will always lie, one will always tell the truth and one will sometimes tell the truth and sometimes lie.

What is your best strategy to choose the door with the car?

[See the rules in the display case (PHSC, 2nd floor) for more information.]